定义Definition
有效核电荷是多电子原子中某个电子实际感受到的核电荷,等于核电荷 Z 减去其他电子的屏蔽常数 S:Zeff = Z − S。内层电子对外层电子的屏蔽作用较强。
Effective nuclear charge is the nuclear charge actually felt by a given electron in a many-electron atom: the nuclear charge Z minus the shielding constant S from the other electrons, Zeff = Z − S. Inner electrons shield outer ones strongly.
估算Estimating it
斯莱特规则给出近似的屏蔽常数:同层电子各屏蔽约 0.35,内一层电子各约 0.85,更内层各 1.00(s、p 电子)。例如钠的 3s 电子:S = 8 × 0.85 + 2 × 1.00 = 8.8,Zeff ≈ 11 − 8.8 = 2.2。粗略地说,外层电子的有效核电荷约等于核电荷减去内层电子数。
Slater's rules give approximate shielding: each electron in the same shell shields about 0.35, each in the next shell in about 0.85, and each deeper one 1.00 (for s and p electrons). For sodium's 3s electron, S = 8 × 0.85 + 2 × 1.00 = 8.8, so Zeff ≈ 11 − 8.8 = 2.2. Roughly, the outer electrons feel the nuclear charge minus the number of inner electrons.
解释周期性Explaining periodic trends
同周期从左到右,核电荷每增加 1,同层电子只增加少量屏蔽,外层电子的有效核电荷增大,所以原子半径减小、电离能增大。同族从上到下,有效核电荷变化不大,但电子层增多、离核更远,所以吸引减弱。
Across a period, each unit increase in nuclear charge is only slightly offset by extra same-shell shielding, so the outer electrons feel a larger effective charge; atoms shrink and ionisation energies rise. Down a group the effective charge changes little but the outer electrons are in higher shells further away, so the attraction weakens.
年表Timeline
- 1930
斯莱特提出估算屏蔽常数的规则
Slater proposes rules for estimating shielding constants
- 1963
克莱门蒂与雷蒙迪由自洽场计算给出有效核电荷
Clementi and Raimondi give effective nuclear charges from self-consistent-field calculations
相关公式Formulas
例题Worked example
N 的 2p 电子:S = 4×0.35 + 2×0.85 = 3.10,Z_eff = 3.90。Zn 的 4s:S = 0.35 + 18×0.85 + 10×1.00 = 25.65,Z_eff = 4.35。
N 2p: Z_eff = 3.90. Zn 4s: Z_eff = 4.35.
例题Worked example
Cl:Z_eff = 6.10,r = 0.99 Å → χ = 0.744 + 0.359×6.10/0.98 = 2.98(鲍林 3.16)。
Cl: χ = 2.98 (Pauling 3.16).